On the normality of secant varieties

TL;DR

This paper proves that secant varieties of certain smooth projective varieties are normal, especially for general canonical curves of genus at least 7, using positivity conditions on line bundles.

Contribution

It establishes the normality of secant varieties under positivity assumptions and applies this to canonical curves of genus at least 7.

Findings

Secant varieties of smooth projective varieties are normal under positivity conditions.

Secant varieties of general canonical curves of genus ≥ 7 are normal.

Provides a new criterion for the normality of secant varieties.

Abstract

In this paper, we show that the secant variety to a smooth projective variety embedded by a sufficiently positive line bundle is normal. As an application, we deduce that the secant variety to a general canonical curve of genus at least 7 is normal.